--- a/handouts/ho02.tex	Fri Dec 05 01:00:34 2014 +0000
+++ b/handouts/ho02.tex	Fri Dec 05 17:13:33 2014 +0000
@@ -133,7 +133,7 @@
 with these equivalences and non-equivalences. 
 
 
-For our matching algorithm however the following six
+For our matching algorithm however the following seven
 equivalences will play an important role:
 
 \begin{center}
@@ -333,7 +333,7 @@
 
 \noindent Again the operation $Der$ might help to rationalise
 this algorithm. We want to know whether $abc \in L(r_1)$. We
-do not know yet. But lets assume it is. Then $Der\,a\,L(r_1)$
+do not know yet. But let us assume it is. Then $Der\,a\,L(r_1)$
 builds the set where all the strings not starting with $a$ are
 filtered out. Of the remaining strings, the $a$ is stripped
 off. Then we continue with filtering out all strings not
@@ -492,7 +492,7 @@
 size of regular expressions it needs to handle. This is of
 course obvious because both $nullable$ and $der$ need to
 traverse the whole regular expression. There seems to be one
-more source of making the algorithm run faster. The derivative
+more issue for making the algorithm run faster. The derivative
 function often produces ``useless'' $\varnothing$s and
 $\epsilon$s. To see this, consider $r = ((a \cdot b) + b)^*$
 and the following two derivatives